Home > Algebra calculators > Variation equations calculator - If X Proportion Y, then prove that X^3+Y^3 Proportion X^2Y-XY^2

Method and examples
Variation Equations
For proportional (µ) sign, we use '@' sign for input.
 
1. Find value of variation using given value
Variation
Given
Find
  1. `x prop y` and `x=4,y=2`. Find `x=18,y=?`
  2. `x prop 1/y^3` and `x=16,y=1/2`. Find `x=54,y=?`
  3. `x prop y^3/z` and `x=8,y=4,z=3`. Find `x=?,y=6,z=4`
  4. `x prop yz` and `x=8,y=4,z=3`. Find `x=?,y=6,z=4`
  5. `x prop y^3z` and `x=8,y=4,z=3`. Find `x=?,y=6,z=4`

2. Prove results for given variation
Variation
Prove that
Constant
  1. If `x prop y` then prove that `x^3+y^3 prop x^2y-xy^2`
  2. If `x prop y` then prove that `x^2+y^2+xy prop x^2-y^2`
  3. If `x prop y, y prop z` then prove that `x^3+y^3+z^3 prop xyz`
  4. If `y prop z, x prop y` then prove that `x^3+y^3+z^3 prop xyz`
  5. If `5x-7y prop 6x+3y` then prove that `x prop y`
  6. If `5x+2y prop 3x-7y` then prove that `x prop y`
  7. If `9x-3y prop 4x+5y` then prove that `x prop y`
  8. If `2x^2-3y^2 prop 4x^2+5y^2` then prove that `x prop y`
  9. If `4x^3+5y^3 prop 2x^3-9y^3` then prove that `x prop y`
  10. If `x^2+9y^2 prop xy` then prove that `x prop y`
  11. If `4x^2+9y^2 prop xy` then prove that `x^2+y^2 prop xy`
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